The invention is based on a fuel injection system as defined hereinafter. In a known system of this kind, a single pump with one pump piston, which via a multiple cam executes a plurality of intake and delivery strokes per cam revolution, is provided as the high-pressure feed pump. The distributor valves with which the known pump is provided are electromagnetic valves, which are urged in the closing direction by the electromotive force and in the opening direction by the delivery pressure of the pump piston upon its delivery stroke. The injection onset is controlled by the drop of these magnet valves, while the end of injection is controlled by a shared electromagnetically actuated control valve that is moved to the closing position when acted upon by current and is moved to the opening position by the pump delivery pressure if the supply of current is interrupted. In this case, two magnet valves must be triggered, and the opening and closing characteristics of each of these valves must be adapted to one another. An expensive multiple cam is additionally necessary, which must drive the pump piston for its delivery stroke. This piston has to pump the entire quantity of fuel to be injected.